What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe- matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con- sequence relation coincides with formal provability: By means of a calcu- lus consisting of simple formal inference rules, one can obtain all...

The 1999 Annual Conference of the European Association for Computer Science Logic, CSL'99, was held in Madrid, Spain, on September 20-25, 1999. CSL'99 was the 13th in a series of annual meetings, originally intended as Internat- nal Workshops on Computer Science Logic, and the 8th to be held as the - nual Conference of the EACSL. The conference was organized by the Computer Science Departments (DSIP and DACYA) at Universidad Complutense in M- rid (UCM). The CSL'99 program committee selected 34 of 91 submitted papers for p- sentation at the conference and publication in this proceedings...

Parameterized complexity theory is a recent branch of computational complexity theory that provides a framework for a refined analysis of hard algorithmic problems. The central notion of the theory, fixed-parameter tractability, has led to the development of various new algorithmic techniques and a whole new theory of intractability.

This book is a state-of-the-art introduction to both algorithmic techniques for fixed-parameter tractability and the structural theory of parameterized complexity classes, and it presents detailed proofs of recent advanced results that have not appeared...